Quadratic synchronous transit method

HyperChein has two synch ron ons transit meth ods im piemen ted. The linear synchronous transit method (LST) searches for a maximum along a linear path between reactants and products. It may happen that this method will end up with a structure having two or more negative eigenvalues. The quadratic synchronous transit method (QSTlisan improvement of LST approach and searches for a maximum along a parabola connecting reactants and products, and for a minimum in all directions perpendicular to the parabola. 

Figure 14.5 Illustration of the linear and quadratic synchronous transit methods. Energy maxima and minima are denoted by and , respectively...

In HyperChem, two different methods for the iocation of transition structures are available. The eigenvector following method is appropriate for unimolecuiar processes or any molecular system where a natural vibrational mode of the system tends to lead to a transition state. Synchronous transit methods are especially useful when reactant and product systems are very different, or In cases where It Is desirable to specify a sequence of structures intermediate between reactants and products. Both linear and quadratic synchronous transit methods have been implemented in HyperChem. 

Illustrating the Concepts 264 11.1 Geometry Convergence 264 11.1.1 Ah Initio Methods 264 11.1.2 DFT Methods 267 14.4 Choice of Coordinates 322 14.5 Transition Structure Optimization 327 14.5.1 Methods Based on Interpolation Between Reactant and Product 327 14.5.2 Linear and Quadratic Synchronous Transit 328... 

One-structure interpolation methods coordinate driving, linear and quadratic synchronous transit, and sphere optimization... 

Fig. 4. The linear synchronous transit (LST) and quadratic synchronous transit (QST) methods for finding transition structures R, reactants P, prc ucts TS, true transition structure 1, maximum on LST path (full curveV, 2, minimum perpendicular to LST path 3, maximum on QST path (broken curve). The model surface is constructed from two...

Gradient methods are very efficient for minimizations however, to locate transition structures they must be modified or constrained to overcome the problems caused by the Hessian not being positive-definite. One approach is to partition the AT-dimensional optimization into a one-dimensional space for maximization, and an (N — l)-dimensional space for minimization. This partitioning in effect chooses a transition vector. The transition vector may be fixed, or may be allowed to vary in a restricted manner (e.g. according to a quadratic synchronous transit path). The search for a maximum in the... 

The LST and QST calculations do not actually locate a proper transition state but aim to arrive at structures sufficiently close to it. Ideally, the resulting configuration would lie within the quadratic basin of the first order saddle point and be suitable for input to subsequent transition state searches. However, the synchronous transit methods often yield structures with more than one negative eigenvalue. 

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